If two numbers have to one another the ratio which a square number has to a square number, and the first be square, the second will also be square. For let the two numbers A, B have to one another the ratio which the square number C has to the square number D, and let A be square; I say that B is also square. For, since C, D are square, C, D are similar plane numbers. Therefore one mean proportional number falls between C, D. [VIII. 18] And, as C is to D, so is A to B; therefore one mean proportional number falls between A, B also. [VIII. 8]